derivative f(x)=|2x-3|

解

導関数

f (x) = ∣ 2 x - 3 ∣

\frac{2 ( 2 x - 3 )}{∣ 2 x - 3 ∣}

解答ステップ

\frac{d}{d x} (∣ 2 x - 3 ∣)

連鎖法則を適用:

\frac{2 x - 3}{∣ ( 2 x - 3 ) ∣} \frac{d}{d x} (2 x - 3)

= \frac{2 x - 3}{∣ ( 2 x - 3 ) ∣} \frac{d}{d x} (2 x - 3)

\frac{d}{d x} (2 x - 3) = 2

= \frac{2 x - 3}{∣ ( 2 x - 3 ) ∣} \cdot 2

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ( 2 x - 3 )}{∣ 2 x - 3 ∣}